Quantifier probability logic and the confirmation paradox

Abstract

Exhumation and study of the 1945 paradox of confirmation brings out the defect of its formulation. In the context of quantifier conditional-probability logic it is shown that a repair can be accomplished if the truth-functional conditional used in the statement of the paradox is replaced with a connective that is appropriate to the probabilistic context. Description of the quantifier probability logic involved in the resolution of the paradox is presented in stages. Careful distinction is maintained between a formal logic language and its semantics, as the same language may be outfitted with different semantics. An acquaintance with sections 1–5 of Hailperin (2006) covering the sentential aspects of probability logic is assumed as background information for quantifier probability logic.